Reconfiguring colorings of graphs with bounded maximum average degree
Abstract
The reconfiguration graph $R_k(G)$ for the $k$colorings of a graph $G$ has as vertex set the set of all possible $k$colorings of $G$ and two colorings are adjacent if they differ in the color of exactly one vertex of $G$. Let $d, k \geq 1$ be integers such that $k \geq d+1$. We prove that for every $\epsilon > 0$ and every graph $G$ with $n$ vertices and maximum average degree $d  \epsilon$, $R_k(G)$ has diameter $O(n(\log n)^{d  1})$. This significantly strengthens several existing results.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 DOI:
 10.48550/arXiv.1904.12698
 arXiv:
 arXiv:1904.12698
 Bibcode:
 2019arXiv190412698F
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Discrete Mathematics;
 05C15
 EPrint:
 7 pages